# My, what large numbers you are

The least common multiple of $$2^ {12} \times 3^{23} \times 5^{45}$$, $$2^{23} \times 3^{45} \times 5^{12}$$ and $$2^{45} \times 3^{12} \times 5^{23}$$ can be written as $$2^a \times 3^b \times 5^c$$, where $$a, b$$ and $$c$$ are non-negative integers. What is the value of $$a+b+c$$?

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